In a car race, car A beats car B by 45 km, car B beats car C by 50 km, and car A beats car C by 90 km. The distance (in km) over which the race has been conducted is
Explanation:
Let their speeds be a, b and c respectively and the length of the race be D.
Car A beats car B by 45 kms
∴ ab=DD-45 …(1)
Car B beats car C by 50 kms
∴ bc=DD-50 …(2)
Car A beats car C by 90 kms
∴ ac=DD-90 …(3)
(1) × (2) = (3)
⇒ DD-45×DD-50=DD-90
⇒ D(D-45)(D-50)=1D-90
⇒ D2 – 95D + 2250 = D2 – 90D
⇒ 5D = 2250
⇒ D = 450
Hence, option (b).
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